validated computing

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1: 3.1 Arithmetics and Error Measures

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§3.1(ii) Interval Arithmetic

… ►With this arithmetic the computed result can be proved to lie in a certain interval, which leads to validated computing with guaranteed and rigorous inclusion regions for the results. …

2: Preface

… ►Saunders was responsible for mesh generation for curves and surfaces, data computation and validation, graphics production, and interactive Web visualization. …

3: Bibliography C

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Validated computation of certain hypergeometric functions. ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.

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External Links:

ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§13.29(v), §15.19(v).

Encodings:

BibTeX

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4: Bibliography M

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The computation of elementary functions in radix $2^p$ . Computing 53 (3-4), pp. 219–232.

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Notes:

International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (Vienna, 1993)

External Links:

ISSN 0010-485X, Document, MathReview, ZentralBlatt

Referenced by:

§4.45(i).

Encodings:

BibTeX

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5: Antony Ross Barnett

… ►He is coauthor of the book Computing for Scientists (with R. … ►Barnett served as a Validator for the original release and publication in May 2010 of the NIST Digital Library of Mathematical Functions and the NIST Handbook of Mathematical Functions.

6: B. L. J. Braaksma

… … ► 1934 in Groningen, The Netherlands) is Emeritus Professor in the Institute for Mathematics and Computer Science at the University of Groningen, The Netherlands. … ►Braaksma served as a Validator for the original release and publication in May 2010 of the NIST Digital Library of Mathematical Functions and the NIST Handbook of Mathematical Functions.

7: Bernard Deconinck

… ►He has worked on integrable systems, algorithms for computations with Riemann surfaces, Bose-Einstein condensates, and methods to investigate the stability of solutions of nonlinear wave equations. He is the coauthor of several Maple commands to work with Riemann surfaces and the command to compute multidimensional theta functions numerically. … ►Deconinck served as a Validator for the original release and publication in May 2010 of the NIST Digital Library of Mathematical Functions and the NIST Handbook of Mathematical Functions. …

8: 15.19 Methods of Computation

§15.19 Methods of Computation

… ►For fast computation of $F(a,b;c;z)$ with $a,b$ and $c$ complex, and with application to Pöschl–Teller–Ginocchio potential wave functions, see Michel and Stoitsov (2008). … ►The representation (15.6.1) can be used to compute the hypergeometric function in the sector . … ►The relations in §15.5(ii) can be used to compute $F(a,b;c;z)$, provided that care is taken to apply these relations in a stable manner; see §3.6(ii). … ►The accuracy is controlled and validated by a running error analysis coupled with interval arithmetic.

9: 13.29 Methods of Computation

§13.29 Methods of Computation

… ►The integral representations (13.4.1) and (13.4.4) can be used to compute the Kummer functions, and (13.16.1) and (13.16.5) for the Whittaker functions. In Allasia and Besenghi (1991) and Allasia and Besenghi (1987a) the high accuracy of the trapezoidal rule for the computation of Kummer functions is described. … ►The recurrence relations in §§13.3(i) and 13.15(i) can be used to compute the confluent hypergeometric functions in an efficient way. … ►The accuracy is controlled and validated by a running error analysis coupled with interval arithmetic.

10: Javier Segura

… … ► 1965 in Novelda, Spain) is professor of mathematical analysis at the Department of Mathematics, Statistics and Computation, University of Cantabria, Spain. … ►Segura served as a Validator for the original release and publication in May 2010 of the NIST Digital Library of Mathematical Functions and the NIST Handbook of Mathematical Functions. …